主讲人：Prof. Elaine Crooks（Swansea University, United Kingdom）

时间：2014年6月25日(周三)9:30-11:30

地点：北二区教学楼508教室

摘要：I will first prove the existence of fronts under a sub-quadratic growth condition on the gradient dependence using the comparison principle and sub- and super-solutions, and then discuss an extension to more general gradient dependence via a priori bounds on truncated problems satisfying the sub-quadratic growth condition (based on Crooks,  Adv. Diff. Eqns 8(3) (2003) 279-314). If time allows, I will also give a brief overview of how positive operator and degree theory can be used to prove the existence of additional equilibria of functions satisfying a monotonicity property, and implications of these equilibria for the existence of travelling fronts for monotone reaction-diffusion systems (based on  Crooks,  Nonlinear Analysis 67(7) (2007) 2297-2305).